中文摘要：

针对球面网壳四边形网格划分中四个角点不易处于同一平面的问题,从三点确定一个平面的最基本几何原理出发,提出一种平面四边形网格作图方法,得到的四边形网格不仅处于同一平面而且杆件长度均一致.通过改进四边形网格的划分方法,得到的平面四边形网格与球面的偏差更小.力学性能分析表明,减小四边形网格网壳节点到球面的偏离距离能提高球面网壳结构的承载力.最后将改进四边形网格划分法与国外采用的表面平移法进行比较,发现改进四边形网格划分法不仅能减少节点偏离距离而且能扩大网格划分的曲面范围.

英文摘要：

For quadrangular mesh of spherical reticulated shells, the four nodes of a gird are not easily in a plane. A graphing method of planar quadrangle mesh was presented, aimed at solving this problem. The method is based on the fundamental geometric principle., three points define a plane. The meshed grid will not only have four planar points but could also get members with equal length. A modified method was then proposed to decrease the deviation of nodes to the sphere. Mechanical behavior analysis shows that decrease of deviation of nodes will increase the load capacity of reticulated shells. Finally, a comparison of modified planar quadrangle mesh and surface translation mesh was made. It indicates that the modified pla- nar quadrangle mesh method will decrease the node deviation and can be widely used in free-form surfaces.